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Problems in highly turbulent flow:
1. Rayleigh-Benard
2. Taylor-Couette
3. Boundary layers
4. 2-phase flow
5. Turbulence with phase transitions
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I. RB
• Oregon vs Grenoble controversy: origin?
• Ultimate RB convection: Kraichnan regime?
• Better understanding of aspect ratio dependence
• Understanding of non-Oberbeck-Boussinesq effects
• Understanding of the large scale wind dynamics
• BLs!
• RB with rotation
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II. Taylor-Couette
•Torque vs Reynolds
•Role of BLs
•Ultimate regime
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III. Boundary layers
•Log-law vs Barenblatt
•Coupling BL-bulk
•Role of plumes, structures: exchange of momentum: statistical description
•Roughness of wall: drag reduction
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IV. 2-phase flow: particles & drops in turbulence, clouds
•Clustering, coalescence
•2-way coupling, 4-way coupling
•sink velocity of particles in turbulence
•effective forece models
•Lagrangian vs Eulerian view
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V. Turbulence with phase-transition
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Instrumentation
Probes on microscale: bolometers, aneometers
High-speed 3D PIV: resolution!
Radio particles
Temperature control crucial
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Why now?
High-speed cameras
Data storage and handling in Tbytes
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I. Rayleigh-Benard convection
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RB system “drosophila” of fluid dynamics & pattern formation
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Onset of convection: rolls
(independent of Pr)
Chandrasekhar, Taylor,
late 1930s
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Convection rolls
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Applications
• Convection in earth mantle (Pr = 1021)• Convection in earth kernal• Convection in stars• Convection in the ocean (including thermohaline)• Convection in the atmosphere• Metal production• ….
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Convection in atmosphere
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Convection in the ocean
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Mantle convection
Glatzmeier
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Reversal of magnet field of earth
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Schlieren visualization of global flow
Tong, Xia et al.,
Hongkong
water,
Pr=4,
Ra=5 109
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Role of plumes in RB convection
L.P
. Kad
an
off,
Ph
ys. T
od
ay 5
4(8
), 3
4 (
200
1)
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2D OB-simulation, Pr=4, Ra=106
Ka
zu S
ugiy
am
a, T
wen
te
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2D OB-simulation, Pr=4, Ra=108
Ka
zu S
ugiy
am
a, T
wen
te
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2D OB-simulation, Pr=2540, Ra=106
Gly
cero
l, K
azu
Su
giy
am
a, T
we
nte
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2D OB-simulation, Pr=2540, Ra=108
Gly
cero
l, K
azu
Su
giy
am
a, T
we
nte
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Focus on global scaling laws
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Nu(Ra): Scaling Nu~Ra
= 2/7 (Castaing, Libchaber, Kadanoff, et al., JFM, 1989, Siggia, ARFM 1994)
= 0.31 (Sreenivasan., Nature, 2000)
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Nu(Ra) for large Ra
Chavanne et al., PRL79, 3648 (1997); Niemela et al., Nature 404, 837 (2000)
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Central idea: Splitting of dissipations into bulk and BL contribution
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Decomposition of kinetic and thermal dissipation
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Phase diagram with data points
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Prediciton of Nu(Pr) for large Pr
Ra=1.78 109
Ra=5.62 107
Xia et al, PRL, 2002
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Also Nu(Ra): no (pure) power law!
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Nu(Ra)
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Ahlers et al., PRL 2001
Experimental confirmation that there is no power law in Nu(Ra)!
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Summary of GL theory
•Systematic, Boussinesq-eq. & Prandtl-Blasius based
theory Phase space of RB convection•No power laws as in general BL and bulk contribute
•Power laws only recover asymptotically
• Consistent with experimental observations
Nu (Ra, Pr)
Re (Ra, Pr)